Computer memory can be minimized by using a different storage mode when the coefficient...

Computer memory can be minimized by using a different storage mode when the coefficient matrix is symmetric. An n × n symmetric matrix A = (a_{i j} ) has the property that a_{i j} = a _{j i} , so only the elements on and below the main diagonal need to be stored in a vector of length n(n + 1)/2. The elements of the matrix A are placed in a vector v = (v_k ) in this order: a₁₁, a₂₁, a₂₂, a₃₁, a₃₂, a₃₃, . . . , a_n,n. Storing a matrix in this way is known as symmetric storage mode and affects a savings of n(n − 1)/2 memory locations. Here,

statements.

Write and test procedures

Gauss Sym(n, (v_i ), (l_i ))

Solve Sym(n, (v_i ), (l_i ), (b_i ))

which are analogous to procedures Gauss and Solve, except that the coefficient matrix is stored in symmetric storage mode in a one-dimensional array (v_i ) and the solution is returned in array (b_i ).